Question

The value of $0.1\bar{6}+0.1\bar{5}-0.1\bar{3}$ is:

• A. $$\frac{17}{90}$$
• B. $$\frac{34}{35}$$
• C. $$\frac{23}{63}$$
• D. $$\frac{19}{99}$$

Answer 1

Answer:

$$\frac{17}{90}$$

$0.1\bar{6}+0.1\bar{5}-0.1\bar{3}$

$0.1\bar{6}=0.16666...$

$x=0.16666.....$

$10x=1.66666...$

$10x-x=1.5$

$9x =1.5$

$x=\frac{1.5}{9}$

Similarly,

$0.1\bar{5}=\frac{1.4}{9}$

$0.1\bar{3}=\frac{1.2}{9}$

$0.1\bar{6}+0.1\bar{5}-0.1\bar{3}=\frac{1.5}{9}+\frac{1.4}{9}-\frac{1.2}{9}$

$=\frac{1.5+1.4-1.2}{9}=\frac{1.7}{9}$

$=\frac{17}{90}$